1. Field of the Invention
The present invention relates to a surface acoustic wave element for obtaining a convolution output by utilizing an interaction of a plurality of surface acoustic waves and a communication system using the surface acoustic wave element.
2. Related Background Art
A surface acoustic wave element has received a great of attention as a key device for spread spectrum communication. The surface acoustic wave element is also used in a variety of applications as a real-time signal processing device, and extensive studies have been made on the surface acoustic wave element.
A surface acoustic wave convolver shown in FIG. 1 is known as such a surface acoustic wave element. Input interdigital transducers (comb electrodes) 12 and 13 and an output electrode 14 are formed on a piezoelectric substrate 11 made of Y-cut (Z-propagation) lithium niobate to obtain this element. When electrical signals are supplied to the input transducers 12 and 13, a surface acoustic wave is excited in the piezoelectric substrate 11 and is extracted as a convolution signal at the output terminal 14.
These transducers and output electrode are formed by pattering a conductive material such as aluminum in accordance with photolithography.
In order to extract a convolution output using such a surface acoustic wave convolver, two input signals each having a carrier angular frequency .omega. are input to the input transducers 12 and 13 and are converted into surface acoustic wave signals. These surface acoustic waves propagate on the surface of the piezoelectric substrate 11 in opposite directions. A convolution signal having a carrier angular frequency 2.omega. is extracted from the output electrode 14 by utilizing a physical nonlinear effect of the substrate.
If the above two surface acoustic waves are defined as follows: ##EQU1## a surface acoustic wave as a product of these two input surface acoustic waves appears on the substrate according to the nonlinear effect of the substrate: ##EQU2## This signal is integrated within the uniform output electrode area and is extracted as a signal represented as follows if l be the length of an interaction region: ##EQU3## This integral range can be substantially .+-..infin. when the interaction length is larger than the signal length.
If the following conditions is given: ##EQU4## equation (1) can be rewritten as follows: ##EQU5## The signal is obtained as a convolution signal of the two surface acoustic surface waves.
This convolution mechanism is described in detail in, e.g., Shibayama, "Application of Surface Acoustic Wave", Television 30, 457 (1976).
On the other hand, when two surface acoustic waves propagate on the surface of the substrate in opposite directions, as described above, a bulk wave having a carrier angular frequency 2.omega. which propagates in a direction perpendicular to the surface of the substrate is generated by the physical nonlinear effect of the substrate, as described in Journal of Applied Physics, Vol. 49, No. 12, PP. 5924-5927, 1978.
This bulk wave is reflected on the lower surface of the substrate 11 and returns to the upper surface of the substrate 11. The returning bulk wave is partially extracted by the output electrode 14, and another part thereof is reflected by the upper surface of the substrate 11, propagates toward the lower surface of the substrate, and returns again toward the upper surface upon reflection on the lower surface.
The bulk wave generated toward the lower surface of the substrate is repeatedly reflected by the lower surface of the substrate, and the signal of the reflected wave can be extracted from the output electrode 14, thereby adversely affecting the convolution signal.
On the other hand, in order to suppress the adverse influences by reflection of the bulk wave on the lower surface of the substrate, a surface acoustic wave element having a substrate of a shape tapered toward the propagation direction of the surface acoustic wave is proposed in Applied Physics Letters, Vol. 15, No. 9, PP. 300-302, 1969.
An example of this conventional element is shown in FIG. 2. The same reference numerals as in FIG. 1 denote the same parts in FIG. 2, and a detailed description thereof will be omitted.
The thickness of a piezoelectric substrate 15 in the element shown in FIG. 2 is changed in the propagation direction of the surface acoustic wave.
Since the element shown in FIG. 2 is a tapered element in which the thickness of the substrate is changed in the propagation direction of the surface acoustic wave, the thickness of the substrate is larger than a conventional surface acoustic wave element having parallel upper and lower surfaces of the substrate, resulting in inconvenience. That is, when a surface acoustic wave is to propagate on the substrate and its wavelength is .lambda., the substrate must have a minimum thickness which is several times the wavelength .lambda.. For this reason, when the tapered substrate is employed, the thickness of the substrate at one side is much larger than the thickness of the surface acoustic wave element having the parallel upper and lower surfaces of the substrate, thus posing a problem.
In addition, since a bulk wave reflected by the lower surface of the substrate at a taper angle of the conventional example is extracted as an electrical signal at the output electrode, a convolution signal cannot be extracted at a high S/N ratio.